Continuum damage mechanics models and their applications to composite components of aero-engines

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Yu, Tianhong (2016) Continuum damage mechanics

models and their applications to composite components

of aero-engines. PhD thesis, University of Nottingham.

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Continuum Damage Mechanics Models and

Their Applications to Composite Components

of Aero-Engines

A thesis for the degree of Doctor of Philosophy

Tian-Hong Yu

2016

Composites Research Group, Faculty of Engineering,

The University of Nottingham, Nottingham NG7 2RD, UK

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Acknowledgements

First of all, I would like to thank my supervisor, Prof. Shuguang Li, who shared valuable expertise and provided important guidance to me throughout the course of this research project, which enabled me to achieve significant progress in the last three years. His attention to detail, patience and academic professionalism not only ensured the delivery of high quality supervision to my research project, but also inspired me to tackle technical problems with persistence and confidence, from which I will benefit for the rest of my life.

I would also like to express my gratitude to my co-supervisors. My gratitude goes to Dr. Elena Sitnikova, for her helpful feedbacks on my research work and her comprehensive advice on my thesis writing, and to Dr. Richard Brooks, for his effort to help sourcing the materials for the experimental work.

The generous support from AVIC Commercial Aircraft Engine Co. Ltd. (ACAE), both financially and technically, which made this research project possible, is gratefully acknowledged. My gratitude also goes to my fellow research team members from ACAE, for their support and the quality time we spent together working for a joint research program.

Moreover, I am forever in debt to my parents for the understanding, encouragement and support they provided to me in the last few years, which allowed me to focus on my PhD study.

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Abstract

Built on top of a consistent continuum damage mechanics (CDM) damage representation formulation, a novel damage evolution law based on the concept of damage driving force is proposed for modelling the evolution of matrix damage in UD composites. This damage evolution law has the advantage of allowing different damage evolution constants to be associated with different loading modes (corresponding to the fracture modes in Fracture Mechanics) when dealing with mixed-mode loading conditions, which avoids the unrealistic assumption in many existing theories that different loading modes make the same contribution to damage evolution. A new CDM model for UD composites is developed incorporating this damage evolution law.

Thanks to the laminate test cases designed and conducted in this project, it is found that the damage initiation and propagation related material constants can be determined using these tests. These damage-related material constants served as inputs to the UD composite CDM model.

Apart from the tests on laminates, detailed experimental investigation was carried out regarding damage in two types of layer-to-layer interlock 3D woven composites which are reinforced by IM7 carbon fibre (CF) and E-glass fibre (GF), respectively. The experimental data obtained and the damage processes recorded for these 3D woven composites can serve as a good reference for future interest in this area, since currently only limited studies are available in the literature regarding damage in this type of 3D woven composites.

The new UD composite CDM model is applied to predict intra-laminar damage in laminates and intra-tow damage in the 3D woven composites. Compared to the

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experimental results, it is found that the model produced satisfactory predictions but lacking the capability to predict a severe stress-strain nonlinearity caused by shear.

A new pragmatic continuum damage model is developed to capture the damage effect of inter-tow cracks in the 3D woven composites caused by warp direction tensile loading. This model works in conjunction with the intra-tow damage predicted by the aforementioned UD composite CDM model.

With the successful development of these damage models, a novel damage modelling methodology for textile composites is made possible and implemented in conjunction with the UnitCells© composite characterisation tool [1] and the artificial neural network tool developed in [1]. Through the artificial neural network for data interpolation, the constitutive behaviour of textile composite incorporating the effect of damage can be interpolated for any load combination, which is then readily available for engineering applications.

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List of Figures

Fig. 1-1 Illustration of fan blades and fan case in a turbofan engine [3] ... 1 Fig. 3-1 Rectangular material coordinate system assigned to UD composites

... 62 Fig. 3-2 Stresses for causing planar cracks parallel to fibre direction ... 66 Fig. 4-1 Attachment of the AE sensor ... 81 Fig. 4-2 Typical fibre direction tensile test stress-strain curve of IM7/8552 CF UD laminate ... 86 Fig. 4-3 Typical transverse direction tensile test stress-strain curve of

IM7/8552 CF UD laminate ... 88 Fig. 4-4 Typical final failure of IM7/8552 CF UD laminate in transverse

direction tensile test ... 88 Fig. 4-5 Typical in-plane shear stress-strain curve of IM7/8552 CF UD

laminate ... 90 Fig. 4-6 Typical IM7/8552 CF cross-ply laminate test result: a) stress-strain

curve, b) AE energy plot ... 92 Fig. 4-7 Typical IM7/8552 CF cross-ply laminate failure modes ... 95 Fig. 4-8 Typical IM7/8552 CF QI laminate test result: a) Stress-strain curve,

b) AE energy plot ... 97 Fig. 4-9 Typical IM7/8552 CF QI laminate failure modes ... 98 Fig. 4-10 XZ-plane CT scan images of cured IM7 CF 3D woven composite: a)

original image, b) image with annotation of distinctive regions ... 101 Fig. 4-11 XY-plane CT scan image of cured IM7 CF 3D woven composite 102 Fig. 4-12 YZ-plane CT scan images of cured IM7 CF 3D woven composite: a) at warp curving region, b) at warp-weft interlacing region ... 103 Fig. 4-13 Typical experimental output for IM7 3D woven composite tested

under the warp tension: a) stress-strain curve, b) AE data plot ... 106 Fig. 4-14 Typical microscopic images of IM7 CF 3D woven composite

loaded to 0.2% warp direction strain: a) at warp curving region, b) at warp-weft interlacing region ... 108

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Fig. 4-15 Typical microscopic images of inter-tow cracks in IM7 CF 3D woven composite loaded to 0.35% strain in the warp direction ... 110 Fig. 4-16 Typical microscopic image of inter-tow cracks in IM7 CF 3D

woven composite loaded to 1% warp direction strain ... 111 Fig. 4-17 Typical microscopic image of cracks in IM7 CF 3D woven

composite loaded to warp direction ultimate strain ... 112 Fig. 4-18 Typical final failure of IM7 CF 3D woven composite tested in

warp direction ... 113 Fig. 4-19 Typical IM7 CF 3D woven composite weft direction test result: a)

Stress-strain curve, b) AE data plot ... 115 Fig. 4-20 Typical microscopic images of IM7 CF 3D woven composite

loaded to 0.4% weft direction strain: a) warp curving region, b) warp-weft interlacing region ... 117 Fig. 4-21 Typical microscopic images of transverse cracks in IM7 CF 3D

woven composite loaded to 0.7% weft direction strain: a) warp curving region, b) warp-weft interlacing region ... 119 Fig. 4-22 Typical microscopic images of cracks in IM7 CF 3D woven

composite loaded to weft direction ultimate strain: a) warp curving region, b) warp-weft interlacing region ... 121 Fig. 4-23 Typical final failure of IM7 CF 3D woven composite tested in weft direction ... 122 Fig. 4-24 Typical in-plane shear test stress-strain curve of IM7 CF 3D woven

composite ... 124 Fig. 4-25 Typical deformation of IM7 CF 3D woven composite under

in-plane shear ... 124 Fig. 4-26 XZ-plane CT scan image of cured GF 3D woven composite ... 126 Fig. 4-27 XY-plane CT scan image of cured GF 3D woven composite ... 126 Fig. 4-28 YZ-plane CT scan images of cured GF 3D woven composite: a)

warp curving region, b) warp-weft interlacing region ... 127 Fig. 4-29 Typical GF 3D woven composite warp direction test result: a)

Stress-strain curve, b) AE data plot ... 129 Fig. 4-30 Typical microscopic images of intra-tow cracks in GF 3D woven

composite loaded to 0.25% warp direction strain: a) warp curving region, b) warp-weft interlacing region ... 131

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Fig. 4-31 Typical microscopic images of cracks in GF 3D woven composite loaded to 0.47% warp direction strain ... 132 Fig. 4-32 Typical microscopic images of cracks in GF 3D woven composite

loaded to warp direction ultimate strain ... 134 Fig. 4-33 Typical final failure of GF 3D woven composite tested in warp

direction ... 135 Fig. 4-34 Typical GF 3D woven composite weft direction test result: a)

Stress-strain curve, b) AE data plot ... 137 Fig. 4-35 Typical microscopic images of GF 3D woven composite loaded to

0.23% weft direction strain: a) warp curving region, b) warp-weft interlacing region ... 139 Fig. 4-36 Typical microscopic images of transverse cracks in GF 3D woven

composite loaded to 0.43% weft direction strain: a) warp curving region, b) warp-weft interlacing region ... 140 Fig. 4-37 Typical microscopic images of cracks in GF 3D woven composite

loaded to weft direction ultimate strain: a) warp curving region, b) warp-weft interlacing region ... 141 Fig. 4-38 Typical final failure of GF 3D woven composite tested in weft

direction ... 142 Fig. 4-39 Typical in-plane shear test stress-strain curve of GF 3D woven

composite ... 143 Fig. 5-1 UD composite matrix cracking damage orientation definition ... 147 Fig. 5-2 CDM model operation flowchart ... 152 Fig. 5-3 Single solid element (C3D8) used for the simulation work in

ABAQUS™/Standard ... 157 Fig. 5-4 Stress-strain plot for the case of uniaxial transverse tension and

reloading ... 158 Fig. 5-5 Damage-stress plot for the case of uniaxial transverse tension and

reloading ... 159 Fig. 5-6 Damage variable - damage driving force plot for the case of uniaxial transverse tension and reloading ... 160 Fig. 5-7 Stress-strain plot for the case of uniaxial transverse compression 161 Fig. 5-8 Damage-stress plot for the case of uniaxial transverse compression

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Fig. 5-9 Stresses on the fracture plane for the case of uniaxial transverse

compression ... 162

Fig. 5-10 Damage variable – damage driving force plot for the case of uniaxial transverse compression ... 163

Fig. 5-11 Stress-strain plot for the case of pure transverse shear ... 164

Fig. 5-12 Damage-stress plot for the case of pure transverse shear ... 165

Fig. 5-13 Damage variable -damage driving force plot for the case of pure transverse shear ... 165

Fig. 5-14 Strain-damage plot for the case of pure transverse shear ... 166

Fig. 5-15 Stress-strain plot for the case of pure in-plane shear ... 167

Fig. 5-16 Damage-stress plot for the case of pure in-plane shear ... 167

Fig. 5-17 Damage - damage driving force plot for the case of pure in-plane shear ... 168

Fig. 5-18 Stress-strain plot for the case of fibre direction tension ... 169

Fig. 5-19 Stress-strain plot for the case of fibre direction compression ... 170

Fig. 5-20 Original and edited experimental stress-strain curves for IM7/8552 cross-ply laminate ... 173

Fig. 5-21 Derived ply level stress-strain response for the 90 plies in the IM7/8552 cross-ply laminate ... 175

Fig. 5-22 Relationship between damage and damage driving force for the 90 plies in the IM7/8552 cross-ply laminate ... 178

Fig. 5-23 Stress-strain prediction for IM7/8552 cross-ply laminate with the experimental result ... 180

Fig. 5-24 Different predictions for IM7/8552 cross-ply laminate: a) Laminate level stress-strain curve, b) Damage variable in the 90º plies ... 181

Fig. 5-25 Predictions of transverse stress in the 90º plies in IM7/8552 cross-ply laminate ... 182

Fig. 5-26 Prediction for in-plane shear of IM7/8552 45 laminate: a) Stress-strain response, b) Damage variable ... 183

Fig. 5-27 Ply level stress prediction for in-plane shear of IM7/8552 45laminate: a) Fibre direction, b) Transverse direction ... 185

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Fig. 5-28 Stress-strain prediction for the E-glass/MY750 cross-ply laminate with the experimental result... 188 Fig. 5-29 Prediction for E-glass/MY750 cross-ply laminate: a) Damage

variable, b) Ply stress ... 189 Fig. 5-30 Predictions for in-plane shear of the E-glass/MY750UD laminate: a)

Stress-strain curve, b) Damage variable ... 192 Fig. 6-1 Predicted stress-strain behaviour for the IM7/8552 QI laminate ... 196 Fig. 6-2 Damage prediction for the 45 and 90 plies in the IM7/8552 QI

laminate ... 197 Fig. 6-3 Ply stress prediction for IM7/8552 QI laminate: a) 90 ply, b) 45

ply ... 198 Fig. 6-4 Prediction for IM7/8552 cross-ply laminate test case reported in [197] ... 199 Fig. 6-5 Prediction for E-glass/MY750 [45º] laminate: a) Stress-strain

response, b) Damage variable ... 201 Fig. 6-6 Ply stress prediction for E-glass/MY750 [45º] laminate: a) Fibre

direction, b) Transverse direction ... 202 Fig. 6-7 Stress-strain plots of biaxial tensile test on E-glass/MY750 [55º]

laminate ... 203 Fig. 6-8 Damage variable VS strain in the X-direction for biaxial tensile test

on E-glass/MY750 [55º] laminate ... 204 Fig. 6-9 Ply stress prediction for biaxial tensile test on E-glass/MY750 [55º]

laminate ... 204 Fig. 6-10 Ply Stress-strain plots for uniaxial tensile test on E-glass/MY750

[55º] laminate ... 205 Fig. 6-11 Damage prediction for uniaxial tensile test on E-glass/MY750

[55º] laminate ... 206 Fig. 6-12 Ply stress prediction for uniaxial tensile test on E-glass/MY750

[55º] laminate ... 207 Fig. 6-13 Unit cell model for the 3D woven composites showing mesh of

warp tows (red), weft tows (green) and pure matrix material (blue) .... 210 Fig. 6-14 Microscopic level unit cell model for predicting effective tow

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Fig. 6-15 Stress-strain prediction for the IM7 CF 3D woven composite under warp direction tension ... 222 Fig. 6-16 Tow longitudinal stress contour plot for the IM7 CF 3D woven

composite under warp direction tension ... 223 Fig. 6-17 Damage variable contour plot for IM7 CF 3D woven composite

under warp direction tension ... 223 Fig. 6-18 Weft tow damage variable contour plot and the selected element

for result inspection ... 224 Fig. 6-19 Damaged weft tow element result: a) Stresses on the fracture plane, b) Damage variable ... 225 Fig. 6-20 Weft tow stress contour plot for the IM7 CF 3D woven composite

under warp direction tension: a)



₃, b)



₂, c)



₁₃ ... 226 Fig. 6-21 Tow deformation prediction (scaled up) for the IM7 CF 3D woven

composite under warp direction tension ... 227 Fig. 6-22 Warp tow damage variable prediction and the selected warp tow

element for result inspection ... 228 Fig. 6-23 Damaged warp tow element output result: a) Stresses on the

fracture plane, b) Damage variable ... 229 Fig. 6-24 Warp tow stress contour plot for the IM7 CF 3D woven composite

under warp direction tension: a)



₁₂, b)



₂₃ ... 230 Fig. 6-25 Stress-strain prediction for the IM7 CF 3D woven composite under

weft direction tension ... 232 Fig. 6-26 Tow longitudinal stress contour plot for the IM7 CF 3D woven

composite under weft direction tension ... 233 Fig. 6-27 Tow deformation prediction (scaled up) for the IM7 CF 3D woven

composite under weft direction tension ... 233 Fig. 6-28 Damage variable contour plot for the IM7 CF 3D woven composite under weft direction tension ... 234 Fig. 6-29 Damaged warp tow element output result: a) Stresses on the

fracture plane, b) Damage variable ... 235 Fig. 6-30 Warp tow



₃ contour plot for the IM7 CF 3D woven composite

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Fig. 6-31 Stress-strain prediction for the GF 3D woven composite under warp direction tension ... 237 Fig. 6-32 Tow longitudinal stress contour plot for the GF 3D woven

composite under warp direction tension ... 238 Fig. 6-33 Damage variable contour plot for the GF 3D woven composite

under warp direction tension ... 238 Fig. 6-34 Damage variable in the weft tows for the case of (a) IM7 CF 3D

woven composite, (b) GF 3D woven composite under warp direction tension ... 239 Fig. 6-35 Damaged weft tow element output result: a) Stresses on the

fracture plane, b) Damage variable ... 240 Fig. 6-36 Weft tow stress contour plot for the GF 3D woven composite under warp direction tension: a)



₃ , b)



₂ , c)



₁₃ ... 242 Fig. 6-37 Tow deformation prediction (scaled up) for the GF 3D woven

composite under warp direction tension ... 243 Fig. 6-38 Warp tow damage variable prediction and the selected element 243 Fig. 6-39 Damaged warp tow element output result: a) Stresses on the

fracture plane, b) Damage variable ... 244 Fig. 6-40 Warp tow stress contour plot for the GF 3D woven composite

under warp direction tension ... 245 Fig. 6-41 Stress-strain prediction for the GF 3D woven composite under weft direction tension ... 246 Fig. 6-42 Tow longitudinal stress contour plot for the GF 3D woven

composite under weft direction tension ... 246 Fig. 6-43 Damage variable contour plot for the GF 3D woven composite

under weft direction tension ... 247 Fig. 6-44 Damaged warp tow element output result: a) Stresses on the

fracture plane, b) Damage variable ... 248 Fig. 6-45 Warp tow



₃ contour plot for the GF 3D woven composite under

weft direction tension ... 249 Fig. 7-1 Graphical example showing the assumption for quantifying inter-tow crack damage effect ... 254

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Fig. 7-2 CT scan images of the IM7 3D woven composites showing material symmetry ... 256 Fig. 7-3 CT scan images of the GF 3D woven composites showing material

symmetry ... 257 Fig. 7-4 3D woven composites unit cell model with artificially introduced

inter-tow cracks showing mesh of warp tows (green), weft tows (blue), interfacial elements (yellow) and pure matrix material (grey) ... 261 Fig. 7-5 Side view of the unit cell model showing mesh of warp tows (green), weft tows (blue), interfacial elements (yellow) and matrix material (grey) ... 261 Fig. 7-6 Example of the GF 3D woven composites inter-tow crack damage

development under increasing warp direction loading ... 263 Fig. 7-7 Interfacial element mesh with yellow-coloured elements simulating

inter-tow crack development ... 264 Fig. 7-8 Assumed warp direction stress-strain responses for the verification

case ... 277 Fig. 7-9 Assumed warp direction stress-strain responses for the verification

case ... 279 Fig. 7-10 Predicted warp direction stress-strain response for the verification

case ... 282 Fig. 7-11 Comparison between the unit cell analysis prediction and the

experimental result ... 283 Fig. 7-12 Empirical relationship between



_DX and



DX ... 285

Fig. 7-13 Comparison between predictions for stress-strain response ... 287 Fig. 7-14 Comparison between the unit cell analysis prediction and the

experimental result for stress-strain responses ... 288 Fig. 7-15 Empirical relationship between



_DX and



DX ... 290

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List of Tables

Table 2-1 Summary of UD composite failure criteria ... 28

Table 2-2 Components in the CDM models for UD lamina ... 38

Table 2-3 Classification of CDM models for UD lamina with regard to the representation of coupled damage effect between E2 and G12 ... 41

Table 2-4 Classification of CDM models for UD lamina with regard to damage evolution laws ... 45

Table 4-1 Video strain gauge parameter summary ... 80

Table 4-2 Acoustic emission equipment parameter summary ... 82

Table 4-3 Laminate specimen summary* ... 83

Table 4-4 Aluminium alloy end tab information for laminate specimens* .. 84

Table 4-5 Cured IM7/8552 CF UD prepreg material property summary [187] ... 85

Table 4-6 IM7/8552 CF UD laminate fibre direction test result ... 86

Table 4-7 IM7/8552 CF UD laminate transverse direction test result ... 87

Table 4-8 IM7/8552 CF UD laminate in-plane shear test result ... 90

Table 4-9 IM7/8552 CF Cross-ply laminate test result ... 91

Table 4-10 IM7/8552 CF QI laminate test result ... 96

Table 4-11 3D woven composites specimen summary* ... 99

Table 4-12 3D woven composites specimen end tab dimension* ... 99

Table 4-13 General information of IM7 CF 3D woven composite [191] .. 100

Table 4-14 IM7 12K carbon fibre tow material properties [189] ... 100

Table 4-15 Cured Gurit Prime™ 20LV epoxy resin material properties [193] ... 100

Table 4-16 Weave pattern geometries of cured IM7 CF 3D woven composite ... 104

Table 4-17 Measured properties of IM7 CF 3D woven composite in warp direction ... 104

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Table 4-19 IM7 CF 3D woven composite in-plane shear test result ... 123

Table 4-20 General information of GF 3D woven composite [192] ... 125

Table 4-21 Sinoma® E-glass fibre tow (75 tex) material properties [195] .. 125

Table 4-22 Weave pattern geometries of cured GF 3D woven composite . 127 Table 4-23 GF 3D woven composite warp direction test result ... 128

Table 4-24 GF 3D woven composite weft direction test result ... 136

Table 4-25 GF 3D woven composite in-plane shear test result ... 143

Table 5-1 UD composite material properties assumed for the verification examples ... 153

Table 5-2 Damage evolution processes assumed for each single mode loading case ... 155

Table 5-3 Damage evolution constants for the verification examples ... 156

Table 5-4 Properties of IM7/8552 UD lamina for damage driving force calculation ... 176

Table 5-5 Damage evolution constants determined for IM7/8552 UD lamina ... 179

Table 5-6 Additional IM7/8552 UD lamina material properties used for laminate analysis ... 179

Table 5-7 E-glass/MY750UD lamina material properties used for laminate analysis ... 187

Table 6-1 Tow volume fractions determined from unit cell models ... 211

Table 6-2 Fibre volume fraction within tows ... 211

Table 6-3 Tow elastic properties for IM7 CF 3D woven composites ... 212

Table 6-4 Tow elastic properties for GF 3D woven composites ... 213

Table 6-5 Effective elastic properties for the IM7 CF 3D woven composite ... 214

Table 6-6 Effective elastic properties for the GF 3D woven composite ... 214

Table 6-7 IM7 carbon fibre tow material properties ... 217

Table 6-8 E-glass fibre tow material properties ... 219 Table 6-9 Cured properties of Gurit Prime™ 20LV epoxy material [193] 221

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Table 7-1 Effective properties of IM7 CF 3D woven composites with

artificially introduced inter-tow cracks ... 264

Table 7-2 Effective properties of GF 3D woven composites with artificially introduced inter-tow cracks ... 265

Table 7-3 Averaged values for ratios of damage variables ... 267

Table 7-4 Assumed stress-strain data for the verification case ... 276

Table 7-5 Damage data extracted from Fig. 7-8 ... 278

Table 7-6 Data produced by the damage model ... 281

Table 7-7 Inter-tow damage data extracted from Fig. 7-11 ... 284

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Abbreviations

2D Two-dimensional 3D Three-dimensional AE Acoustic emission CF Carbon fibre

CDM Continuum damage mechanics

CFRP Carbon fibre reinforced plastics

FAA Federal Aviation Administration

GE General Electric company

GF E-glass fibre

GFRP Glass fibre reinforced plastics

Micro-CT Micro computed tomography

Prepreg Pre-impregnated composites

QI Quasi-isotropic

RTM Resin transfer moulding

RVE Representative volume element

UD Unidirectional fibre-reinforced composites

UMAT User-defined material subroutine

VARTM Vacuum assisted resin transfer moulding

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Notations



Direct stress component



Shear stress component



Direct strain component



Engineering shear strain component

 Poisson’s ratio

E Young’s modulus

G Shear modulus

U Complementary strain energy density function

 Helmholtz free energy density I Irreducible integrity bases

V Damage vector



Damage variable defined for UD composite material system



Damage variable defined for textile composites

S

Material compliance matrix

C

Material stiffness matrix

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1. Introduction

1.1 Background

As mentioned in [2], to improve the propulsive efficiency of aerospace turbofan engine for achieving better fuel economy, modern turbofan engines are designed with increasingly large fan sections. As shown in Fig. 1-1, for a typical fan section of a turbofan engine, the fan blades and fan case are the two major structural components.

Fig. 1-1 Illustration of fan blades and fan case in a turbofan engine [3]

With the increase in size, fan sections of modern turbofan engines are becoming heavier. For example, the CF-6 engine produced by General Electric (GE) Aviation, which entered service in 1973, had a bypass ratio of 5. The fan section in that engine weighs about 820 kg and is equivalent to approximately 20% of the total engine weight. By the time of 2011, the new GEnx turbofan engine, which is developed as a modernised replacement for the CF-6 engine, featured a bypass

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ratio of 10. This time, the fan section in the GEnx engine weighs about 1742 kg and accounts for roughly 30% of the total engine weight. As can be seen, the increase in size for the fan section has caused significant weight penalties. Moreover, every kilogram added to the fan section normally results in 2.25 kg of extra support structure being incorporated into the engine and aircraft wing structures [2].

To reduce the weight penalty associated with large fan section, light-weight composite materials are used in the fan sections of modern turbofan engines. According to [4] and [5], in the case of GEnx engine, the carbon fibre composite fan blades and fan case employed saved engine weight by about 160 kg per engine when compared to the metallic alternative.

Apart from weight-saving, impact resistance is another important consideration for fan blades and fan case. This is due to the aircraft engine certification requirements imposed on fan blades and fan case for the safe operation of commercial flights. For example, the Federal Aviation Administration (FAA) in the United States of America requires that fan case of a turbofan engine must be able to contain failed and released fan blades when the engine is running at full power. This dictates that the fan case must have sufficient impact resistance to prevent the penetration of high speed blade fragments through the fan case [6]. Because of this, the fan case of a turbofan engine is often referred to as the fan containment case. In addition, fan blades are also subjected to bird strike requirements. For instance, during a typical take-off scenario, if the fan blades are impacted by a bird below a certain size and weight, the damaged fan blades should not cause engine thrust reduction higher than the limits specified in related certification requirements, like those in [6].

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As a result, for the design of composite fan blades and composite fan case, one should consider impact damage resistance from the start of the design process. Moreover, to predict impact damage accurately and efficiently during the design process of composite structural components, a robust and systematic composite damage modelling strategy is required.

According to [7] and [8], initially, in the engineering community, there was little interest in predicting damage in composites and only simple failure prediction methods were used for the design and sizing of laminated composites. The common practice at that time was to use fibre failure strain to predict the final failure of laminates or to adopt the “make and test” approach to measure laminate failure stress (strain) allowables directly. The former method may be acceptable for quasi-isotropic (QI) laminates since there are sufficient numbers of fibres in multiple directions, making the laminate behaviour as fibre-dominated. This method was in particular favoured by those engineers who treated carbon fibre composites as “black aluminium” where QI laminate stacking sequences were used exclusively when designing the laminates [9]. However, to exploit the full potential of laminated composites, stacking sequences other than QI should be used where appropriate. For the laminates where matrix failure modes are important, the former method is not suitable and the “make and test” approach is normally used in the industry to provide information on laminate failure [7]. However, this approach is both time-consuming and expensive as it is not a predictive method and a large number of tests on laminate samples of different stacking sequences are necessary in order to obtain corresponding failure stresses (strains) [8]. As a result, there is a growing trend in the engineering community to

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move away from the “make and test” approach and rely more on the predictive methods for laminate failure analysis [7].

In response to this need of predictive laminate failure analysis methods, various failure criteria applicable to the unidirectional (UD) laminae inside laminates were developed. These criteria were later assessed in a series of World Wide Failure Exercises (WWFEs). However, it was found that instead of simple instantaneous failures, many laminates suffered gradual damage processes when subjected to loads [10]. Due to this and as a recommendation resulting from the WWFE activities, the laminate failure theories incorporating damage process modelling capabilities have been found to be superior for characterising laminate behaviour under loads [10-12]. Furthermore, another important conclusion from the WWFE activities is that failure criteria and damage modelling formulations should be physically based to reflect the true physics of failure and damage in composites [9,10,13]. It was identified that many existing laminate failure and damage theories contained deficiencies which compromised the physical justification of these theories, leading to inaccurate predictions in some cases [12,14]. These deficiencies should be rectified before the failure and damage theories can be approved for engineering applications.

Apart from laminates, textile composites are also gaining applications in the fan sections of turbofan engines. A recent example is the CFM Leap-X engine developed by Safran Aircraft Engines [15], which used 3D woven carbon fibre composites to construct the fan blades and the fan case. Due to the novelty and the more complex internal structures of 3D textile composites relative to conventional laminated composites, failure and damage analysis of 3D textile composites is not as well-developed as that for laminates. Consequently, no systematic approach

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suitable for engineering applications was provided in the open literature regarding failure and damage analysis of 3D textile composites.

Based on the background information as introduced above, it can be seen that with the increasing application of composite materials in aircraft engines, especially with the use of novel textile composites, there is a genuine and urgent need in the aerospace industry for a physically rigorous, efficient and systematic composite damage modelling methodology to aid the design process of composite structures, which to the best of author’s knowledge is not yet available in the engineering community. Moreover, as composites of different reinforcement configurations might be considered for aero-engine applications, such a methodology should be applicable to simple forms of composites like conventional laminates, as well as advanced textile composites like 3D textile composites.

1.2 Aims & Objectives

In response to the aforementioned demand from the aerospace industry, the aim of this research is to develop a physically based, efficient and systematic damage modelling methodology for composite structures in aero-engines, with an emphasis on the damage analysis of textile composites.

The development of this methodology is a part of the joint research effort to establish an integrated tool set for the design and analysis of composite structures in aero-engines. Due to this, the damage modelling methodology developed here serves as a necessary input to the textile composite characterisation toolbox developed in [1], where the characterisation of failure and damage in textile composites is made possible thanks to the adoption of this methodology. With the

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failure and damage effect properly accounted for, the material properties predicted by the material characterisation toolbox are then used in the composite structure impact analysis models developed in [16], where impact damage in various composites structures is simulated and assessed to aid the design of these structures.

To accomplish the research aim stated above, following objectives are set:

(1) To develop a novel physically based theoretical damage model for UD composites. This model should be capable of rationally predicting the orientation, initiation and evolution of matrix damage, as well as detecting abrupt failure modes like fibre failures. Moreover, it should be applicable to general loading conditions including unloading and reloading scenarios. (2) To implement the aforementioned UD composite theoretical damage model as

practical material subroutine codes usable for damage analysis, which are catered for the prediction of damage in UD laminae within laminates, as well as for the prediction of damage in UD fibre tows inside textile composites. (3) If applicable, to develop a pragmatic damage model to account for possible

interfacial damage associated with the interfaces between the fibre tows and the matrix materials.

(4) To carry out experimental investigation regarding damage in laminates and textile composites. For the experimental work, different test cases should be designed and employed respectively for the determination of damage-related material properties and the acquisition of reference experimental data which can be used to validate the damage models developed in this research.

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(5) To verify that the damage models and the material subroutines developed in this research work are mathematically rigorous and self-consistent using simple analysis cases where the correctness of the results can be judged based on common sense and analytical results.

(6) To carry out validation work for the damage models developed in this research. This can be achieved by applying the damage models for the prediction of real-life damage scenarios concerning laminates and textile composites. The predictions from the models should then be compared against the corresponding experimental data recorded so that the model performance can be evaluated and validated.

1.3 Structure of Thesis

There are eight chapters in this thesis. Apart from the current introduction chapter, the organisation for the rest of the chapters is described below.

In Chapter 2, a comprehensive and up-to-date literature review is provided for the topics relevant to this research. These topics include the background and development of aerospace composites, the investigation of failure and damage in composites of various fibre reinforcement configurations, and the theories and modelling techniques developed for predicting failure and damage in composites. Some important observations are made based on the literature review conducted, which provided valuable guidance for the present research.

Based on the appraisal of UD composite failure and damage theories as presented in the literature review, a novel theory for modelling matrix damage evolution in UD composites is developed and described in detail in Chapter 3.

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In Chapter 4, the experiments conducted on the laminates and the 3D textile composites for this research project are introduced. The experimental results obtained from different test cases enabled the determination of damage-related material properties and provided reference experimental data which can be used to validate the damage model predictions.

The damage evolution law introduced in Chapter 3 is integrated with an existing UD composite failure criterion and an existing UD composite damage representation formulation to form a novel continuum damage mechanics (CDM) model applicable to UD composites. The implementation and the verification of this CDM model are presented in Chapter 5.

In Chapter 6, the validation of the novel UD composite CDM model is conducted. Through the validation work, the suitability of this CDM model to predict real-life composite damage scenarios is assessed, demonstrating the advantages and deficiencies of this model when used for practical applications.

A pragmatic damage model developed for capturing inter-tow damage effect is introduced in Chapter 7. This damage model is developed to complement the UD composite CDM model for situations when the effect of inter-tow damage like tow-matrix inter-facial debonding cannot be ignored in the process of damage analysis.

Finally, in Chapter 8, the conclusions and outcomes of this research are summarised. Based on the findings out of this project, suggestions for future research directions in this research area are also provided.

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2. Literature Review

In this chapter, a comprehensive and up-to-date literature review is provided for the topics relevant to this research.

Since this research focuses on the composite materials for aerospace applications, an overview on the background and the development of aerospace composites is provided in this chapter.

Furthermore, as the aim of this research is to develop a composite material continuum damage mechanics model intended for engineering applications, experimental investigations and theoretical developments concerning failures and damage in composites are reviewed. Such review is presented in this chapter according to the order of increasing complexity of composite materials, i.e. from the simplest unidirectional (UD) composites to the more advanced 3D textile composites.

2.1 Composite Materials for Aerospace Applications

In this section, a review on the use of composite materials in the aerospace industry is presented.

First of all, to appreciate the rationale behind the increasing applications of composite materials in the aerospace industry, a general discussion on the benefits of using composites is provided, along with a brief summary for the historical developments associated with aerospace composites.

Then, the shortfalls and issues related to the most common type of aerospace composites, laminated composites, are discussed. This then leads to the review of

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3D textile composites, where the reasons for its increasing popularity over laminates for certain applications are explained.

2.1.1 Benefits and History

According to [17,18], initial serious application of composites in the aerospace industry dates back to the 1960s, when high performance continues fibres and homogeneous matrix material were first combined together to form the so called advanced composite material at that time. Among the composite materials reinforced by different fibre types, the one reinforced by carbon fibres, i.e. carbon fibre reinforced plastics (CFRP), has received the widest range of applications. In comparison to aluminium alloys, which are the most common metallic materials traditionally used in aerospace industry, CFRP has many superior properties.

First of all, specific stiffness and specific strength in the longitudinal direction of typical unidirectional (UD) CFRP are normally about 3 and 6 times higher than those offered by aluminium alloy [17]. This often allows significant weight savings to be achieved when switching from traditional metallic structures to composites structures. For almost any aerospace vehicle, weight saving is normally always beneficial as either extra payload can be accommodated or significant reduction in fuel consumption can be achieved. In the case of commercial airliners, extra payload capability may allow more passengers to be carried per flight to maximise airline profit, or alternatively, without using the additional payload capability, a resulting lighter aircraft leads to lower specific fuel consumption which reduces the direct operating cost of commercial flights. As mentioned in [17], according to the statistics in 1990, the value of weight

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savings for various aerospace vehicles can be translated into corresponding life cycle fuel cost savings, which varies from a sizable $300/lb for a medium-sized helicopter to an astonishing $30,000/lb for a spacecraft. Based on this, the attractiveness of using composites for achieving lighter aerospace structures is obvious.

Other than weight saving, composites can also be tailored to suit specific structural load requirements. A well-known example is the Grumman X-29A experimental aircraft which had forward-swept wings. The forward-swept wing structures were made with composites which contained CFRP laminates with layers tailored to overcome the static divergence associated with this particular wing configuration, which cannot be practically achieved using traditional isotropic materials [18].

Composites are also known to be of better fatigue resistance than aluminium alloys. Typically, CFRP has much longer fatigue life than aluminium alloys. In composites, fatigue damage accumulation is normally in the form of slow development of multiple damage modes that are wide-spread in the material. On the contrary, in metallic materials, fatigue loading often induces a few dominant microcracks which may propagate abruptly when a critical number of fatigue cycles is reached [18]. As a result, metal fatigue is normally more abrupt and dangerous than composite fatigue.

Another advantage of using composites is that large integrated structural components can be made possible thanks to composite manufacture processes like co-curing. This may significantly reduce the numbers of parts and fasteners in a structural assembly. As illustrated in [17], the CFRP composite structure replacement for the original full metallic vertical tail plane of L-1011 airliner not

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only saved 27% structural weight, but also reduced the part number and fastener number down to a third and a quarter of the original quantities respectively. This certainly reduced structural complexity and simplified the assembly process dramatically. Moreover, integrated composite structures may even improve aerodynamic performance directly. In the case of the F-22 fighter jet, some flight control surfaces were made with composites such that the control surface skins were co-cured to the supporting structures underneath. Thanks to this, no rivets were used on the skins which led to less aerodynamic drag [18].

Due to the benefits offered by composite structures as listed above, increasing applications of composite materials in the aerospace industry started around the 1960s. Initially, owing to limited experience with composites, by the time of the 1970s, attempts were only made to produce trial composite parts for replacing existing metallic structures. These early attempts include CFRP replacement structures for metallic control surfaces and sections of empennage primary structures on the Boeing 727, the Lockheed L-1011 and the McDonnell Douglas DC-10 transport aircraft [17].

Then, in the 1980s, thanks to the experience gained from earlier attempts, composite structures were designed from the start as production pieces for control surfaces, winglets and empennage structures of airliners. The Airbus A300/310 and A320 aircraft family, as well as the Boeing 757/767 and 777 aircraft, were some of the famous commercial aircraft types at that time which utilised substantial CFRP and sandwich composite materials [17].

By the time of 2009, CFRP composites had secured dominant presence in aircraft structures as not only most of the secondary structures and empennage structures were made of composites, but major primary structures like fuselage and wings

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were also mainly constructed from CFRP. The latest examples are the Boeing 787 [19] and the Airbus A350 [20] airliners as both are flying with nearly complete CFRP airframes. It is truly remarkable considering that just after 50 years of development since 1960, CFRP had gained such a wide range of applications in aircraft structures to an extent that landing gear and engine pylon might be the only major aircraft structural components without extensive use of CFRP.

In terms of composite applications in aerospace turbofan engine, the trend is more conservative. The service temperature limit of polymer matrix composites effectively constrained the application of composites to “cold” sections of engines. As a result, composites are normally only employed for structures in the fan system.

Initially, around 1990, for limited types of engines, composites were only used in the nose cone which is the foremost component positioned in the fan system for guiding air stream into the engine air intake [2].

By the time of 1993, General Electric (GE) first successfully used CFRP laminates for making large fan blades for the GE90 turbofan engine. The laminates were composed of hundreds of pre-impregnated (prepreg) layers, which were moulded and cured into the blade shape required. In addition, a thin layer of titanium alloy is attached to the blade leading edge for shielding the laminates from impact and erosion damage. This marked the start of large quantity applications of composites in aero-engines [2]. Since then, composites were used in other turbofan engine components like fan containment case and bypass air duct stator vanes.

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In 2006, the first composite fan containment case design emerged, which was employed on the GEnx turbofan engine. According to [21-23], this composite fan case design selected 2D tri-axial braided carbon fibre fabric as the fibre reinforcement type which was rolled into a cylinder. The cylinder was then moulded into fan case structures using resin transfer moulding (RTM) process. For each fabric layer, fibre tow orientations were set at -60º, 0º and 60º to form a quasi-isotropic material architecture. It was argued that since every fabric layer was quasi-isotropic, stiffness mismatch between layers would be minimised which should help to prevent inter-laminar damage. However, other than stiffness mismatch, weak interlaminar strength is also a major cause for delamination damage. Since the 2D tri-axial braided fabric still retained the layered configuration where the inherently weak interfaces between the layers were still present, it is envisaged that this woven architecture should still be susceptible to delamination damage.

Just seven years later, in 2013, 3D woven CFRP composites were successfully employed in the fan blade and the fan case structures of the new CFM Leap-X turbofan engine, which is expected to enter into service by 2016 [15].

2.1.2 Issues Associated with Laminates

However, the use of composite materials in the aerospace industry is not without problems and hurdles.

For laminated composites, which are the most commonly used type of composite materials, although they possess superior in-plane mechanical properties, their poor through-the-thickness properties can be a significant drawback [24,25].

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Since there is no fibre reinforcement in the thickness direction, laminates have low Young's modulus and strength values in the thickness direction. For the same reason, their transverse shear modulus and strength are also low. Moreover, because of their layered architecture and low inter-laminar fracture toughness, laminates are known to be prone to delamination damage which can be easily caused by inter-laminar shear stresses arising from transverse impact. As a result, laminates usually have poor impact damage resistance.

A well-known example demonstrating the inferior impact resistance of laminates is the ill-fated development of CFRP fan blades for the Rolls-Royce RB211 turbofan engine. Developed in the 1960s, these fan blades were made of carbon fibre laminates and represented a radical new advancement in aero-engine technology at that time [26]. However, the development ceased when the blades shattered catastrophically under bird strike during the engine bird ingestion test [27]. Due to this composite fan blade design flaw and other technical issues, the RB211 engine programme suffered long delays and heavy financial penalties which led to the nationalisation of Rolls-Royce. In the end, conventional titanium alloy fan blades replaced the composite blades which then allowed the RB211 engine to enter the service.

According to [25,28], apart from the shortfalls in terms of mechanical properties as mentioned above, there are also many issues concerned with laminate manufacture.

Laminates are mostly made from prepregs which require expensive refrigeration facilities for storage. This normally causes significant increase in the production cost.

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Beside this, laminate manufacture can be very labour intensive as in many cases manual hand lay-up procedure is still required if automation is not possible. A typical example is the making of a CFRP composite fan blade for the GE90 engine, where hundreds of prepreg layers were laid piece by piece by shop floor workers to form the stacking sequence desired [2]. Without a doubt, such a labour intensive process resulted in long production times as currently a single CFRP fan blade for the GE90 engine needs about 340 hours of lead time from the cutting of raw prepreg material to the delivery of a finished blade [29].

In addition, most prepreg layers used for making laminates are poor for draping. As a result, laminates normally cannot be directly moulded into complex shapes and components of complex shapes may have to be carefully machined from laminates which is time-consuming and likely to introduce defect if the process is not well-controlled.

2.1.3 3D Textile Composites

3D textile composites first emerged in the 1960s, when carbon-carbon 3D braided composite was evaluated for its application in rocket motor components [30]. However, it was not until the mid-1980s that 3D textile composites in the form of fibre reinforced polymers received serious development and 3D textile fibre reinforcements of various configurations were developed. The need of 3D composites is mainly to overcome the deficiencies associated with 2D laminates, that is, to improve through-the-thickness mechanical properties, to improve impact damage resistance and to reduce high production cost [31]. However, due to the inherent fibre undulation presenting in most 3D textile composites, they

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normally have inferior in-plane mechanical properties when compared with laminates of similar fibre volume fractions. As a result, 3D textile composites may not be suitable for stiffness- and strength-critical applications where high in-plane mechanical properties are required. Nonetheless, thanks to the benefits offered by 3D textile composites, they are becoming more widely-used in the aerospace industry, especially for structural components requiring good impact resistance. Unlike prepregs, for producing 3D textile composites, large quantities of dry fibre tows are formed into 3D textile preforms using textile processes. The preforms are then impregnated with resin according to liquid moulding processes so that the final composite component can be moulded.

In 3D textile composites, fibres are oriented or inserted in the thickness direction using textile processes such as stitching, 3D weaving, braiding and knitting [32]. With fibre reinforcement in the thickness direction, 3D textile composites have better mechanical properties in the thickness direction and are less prone to delamination when compared against laminates [24,31,32]. Thanks to the textile processes which are automated by the use of textile machinery, preforms of 3D textile composites can be produced at a fast rate with little human interference. Moreover, without much difficulty, some textile processes can be set up to produce single-piece near-net-shape 3D textile preforms of complex shapes [24,32]. Last but not least, due to the combination of automated textile processes and the use of dry textile preforms instead of prepreg materials, the production cost of 3D textile composites is usually much lower than that of laminates.

The simplest and the cheapest textile process for making 3D textile preforms is stitching, where 2D fabric layers are stitched together in the thickness direction by high-strength fibres [24,32]. This type of 3D textile composites are commonly

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referred to as stitched composites. In contrast to other textile processes, stitching is considered as the most flexible process because through-the-thickness fibre reinforcements can be chosen to be applied only at where needed. Stitched composites have been used on centre fuselage skin of the Eurofighter fighter aircraft [33] and rear pressure bulkhead in the Airbus A380 airliner [34,35]. For both cases, it was reported that stitched composites achieved significant cost savings over equivalent prepreg laminate constructions.

3D weaving is the fastest and the most used textile process for producing large volumes of 3D preforms [24,25,28]. More importantly, it is capable of weaving preforms of complex shapes which makes the production of single-piece near-net-shape 3D woven composites possible. However, although a wide range of through-the-thickness weave patterns are available, in-plane fibre tow orientations are normally restricted to 0º and 90º (warp and weft directions). This means 3D woven composites normally have poor in-plane shear properties. The earliest application of 3D woven composites for commercial aviation appeared in the Beech Starship aircraft where 3D woven composite structural connectors were used to join wing panels[36]. Recently, 3D woven composites were used for constructing the fan containment case of the CFM Leap-X turbofan engine where flanges and other structural features were continuously woven together for better structural integrity [37].

3D preforms can also be made using braiding [24,32]. Braided 3D composites normally have the highest level of conformability, structural integrity and torsional stability among all types of 3D composites. The braiding process can be adjusted during operation to achieve variations in cross-sectional shape, taper, and bends for the preform that is being braided. Thanks to the wide range of braiding

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angles available, fibres can be oriented from -80º to 80º in a plane with respect to the braiding axis. However, due to limitations of most braiding machines, this textile process currently can only produce slender preforms. It was reported that propeller blades for a type of naval landing craft had been made from 3D braided composites [38].

Knitting is another textile process for making 3D preforms. Knitted preforms are highly drapable which makes them most suitable for producing net-shape parts of very complex geometry [24,32]. However, due to the highly curved fibre path resulting from the knitting process, knitted 3D composites usually have low stiffness when compared with other types of 3D composites. Because of this, knitted 3D composites are mainly used for non-structural components.

Aforementioned 3D textile composites generally have better impact damage resistance than laminates.

For 3D woven composites, it was found that the impact energy required to initiate damage can be up to 60% higher than that for laminates of the same thickness [39]. Moreover, mode I type of fracture toughness values of 3D woven composites can be 6 to 20 times higher than those offered by laminates of the same thickness, resulting in improved resistance to impact-induced delamination [40,41]. In some cases, impact energy dissipation in 3D woven composites was found to be more than twice of that in laminates of comparable areal densities and fibre volume fractions under low speed impact scenarios with a fixed impact speed of 2m/s [42]. When compared with laminates, better impact damage resistance of 3D woven composites often leads to less impact-induced degradation for in-plane mechanical properties, hence, providing better residual properties after impact [43,44]. However, due to crimping of fibres, damage to fibres during

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weaving processes and the existence of resin rich areas, 3D woven composites normally have lower in-plane mechanical properties than laminates of the same fibre volume fraction [43-52].

In terms of stitched composites, their improved impact resistance over laminates was reported in [53-57] for low speed impact events and in [58-60] for high speed impacts. Detailed studies on the influence of various stitch parameters to the impact resistance of stitched composites were presented in [61,62]. It was found a small volume fraction of through-the-thickness stitched fibre reinforcement is normally able to provide significant increase in mode I interlaminar fracture toughness. As a result, crack propagation in stitched composites mostly occurs in mode II type of fracture. However, similar to 3D woven composites, compared with laminates of the same fibre volume fraction, stitched composites usually have reduced in-plane mechanical properties [32,59,63-66]. This is because the needles for the stitching process often damage the in-plane fibres locally. Also, resin rich zones exist in stitched composites which are normally associated with the thickness direction threads.

According to [67,68], thanks to their tight integral textile structure, 3D braided composites were found to have the smallest damage areas under ballistic impacts when compared to all other 3D textile composites tested. Moreover, they were also reported to have the highest ballistic impact penetration resistance among all the textile composites studied in [69]. Under low speed impact, since there is no layered architecture in 3D braided composites, resin crack, tow debonding and fibre breakage were the common failure modes observed, while delamination was never discovered [70-73]. Due to curved fibre tows around the braiding axis, 3D

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braided composites also have lower in-plane properties than laminates of the same fibre volume fraction [67,74].

In terms of knitted 3D composites, although the highly curved fibre tow path limited their in-plane material properties, they were reported to have the ability to absorb substantial amount of impact energy, largely due to high mode I fracture toughness [31]. As mentioned in [75], compared to the composite of uniweave reinforcements with similar fibre volume fraction, the knitted 3D composite used in that investigation was shown to absorb 64% more impact energy when tested under impacts with an incident energy of 7.3J. Chou et al. [76] conducted notched Charpy impact tests on the E-glass/epoxy composites of 3D knitted architecture and plain weave architecture. They found that for the test case they designed, the impact energy absorbed by the former was about 2.4 times of that absorbed by the latter. As suggested in [31], this ability of knitted 3D composites to absorb much greater amounts of impact energy than 2D composites implies that they are potential candidate materials for damage-prone structures or crush members.

2.2 Failure in UD Composites under Static Loadings

In this section, failure mechanisms and failure theories related to the simplest form of composites, UD composite, are reviewed.

Since most high performance fibre-reinforced composites are comprised of UD composites in the form of tows or UD laminae, a good understanding of the failure mechanisms associated with UD composite is normally beneficial for the failure and damage analysis of composites with more advanced reinforcement architectures.

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As pointed out in [35] and [7], due to the brittle nature of composites, independent UD composites are normally considered to fail abruptly instead of showing a gradual damage process. As a result, failure theories for UD composite are abundant in the literature.

However, as will be discussed later, when UD composites are bonded together to form composites of more complex reinforcement architectures, gradual damage phenomenon becomes more influential.

2.2.1 Failure Mechanisms

As summarised in [77], UD composite exhibits different failure modes depending on the loading conditions and the properties of the constituent materials.

Under longitudinal tension, the constituent material inside UD composites with the lowest ultimate tensile strain should fail first. Normally, fibres have lower ultimate strains than matrix materials. As a result, longitudinal tension usually leads to fibre tensile failure in UD composites. However, this failure mechanism is normally complicated by the statistical distribution of fibre strength which varies from fibre to fibre and from point to point.

For UD composites under longitudinal compression, common failure modes observed are micro-buckling and fibre kinking. For UD composites with low fibre volume fraction, extensional mode of microbuckling is likely to occur. With increasing fibre volume fraction, shear mode microbuckling or fibre-matrix debonding become the dominant failure modes. If the UD composites is of very high fibre volume fraction and has well-aligned fibres, pure compressive failure might be encountered which is normally in the form of fibre shear failure.